The stochastic variational method and its fixed core variant are applied to the calculation of lithium positride (LiPs), positronic beryllium (e+Be), sodium positride (NaPs) and positronic magnesium (e+Mg). The revised binding energy of LiPs was 0.012 341 Hartree, that for e+Be was 0.031 47 Hartree, that for NaPs was 0.008 419 Hartree and the binding energy for e+Mg was 0.015 612 Hartree. The binding energies for LiPs and e+Be are expected to be within 2% of the variational limit. The uncertainties in the NaPs and e+Mg binding energies are larger and these are expected to be within 10-15% of the variational limit.